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The top of a ladder slides down a vertical wall at a rate of 0.15 m/sec. at the moment when the bottom of the ladder is 3 m from the wall, it is sliding away from the wall at a rate of 0.2 m/sec. how many meters long is the ladder? 5 meters c

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You have x^2 + y^2 = L^2 where x is the distance from the bottom of the ladder to the wall, y is the height of the ladder, and L is the length of the ladder.

Differentiating with respect to t,

2xx' + 2yy' = 0
y' = -0.15, x' = 0.2, x = 3
This gives y = 3*0.2/0.15 = 4

L^2 = 3^2 + 4^2 = 5^2
L = 5m

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